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Math Help - Alebraic Topology - Homotopy

  1. #1
    Junior Member
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    Alebraic Topology - Homotopy

    I'm stuck and I need help, can anybody help me out with this problem,
    Let
    f : I → R^2 be given by f (s) = (1 + s + s^2 − sin(πs), 2/1+s^2) and let
    g : I → R^2 be given by g(s) = (1 + 2s, 2 − s).
    Prove that f ≃ g by explicitly constructing a homotopy.

    I know that H(s,0) = f(s) and H(s,1) = g(s)
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  2. #2
    Senior Member Tinyboss's Avatar
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    R^2 is contractible, so any two curves are homotopic. That should give you a good idea of how to construct the homotopy.
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